ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of ZrHg (Materials Project id mp-2510)

       107      102       89        0        0        0  
       102      107       89        0        0        0  
        89       89      147        0        0        0  
         0        0        0       66        0        0  
         0        0        0        0       66        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 102.33 GPaEV = 100.49 GPaGV = 37.6 GPaνV = 0.33633
ReussKR = 101.23 GPaER = 28.708 GPaGR = 9.8805 GPaνR = 0.45274
HillKH = 101.78 GPaEH = 66.083 GPaGH = 23.74 GPaνH = 0.39179

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 29 GPa 48.374 GPa 66 GPa 66 GPa 307.63 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 9.5293 GPa 129.93 GPa 2.0832 TPa–1 3.8976 TPa–1 2.5 GPa 66 GPa-1.0791.9249Value
Anisotropy 13.64 1.8710 26.4Anisotropy
Axis 1.0000
0.0000
0.0000
0.5049
0.5049
-0.7001
0.0000
0.0000
1.0000
-0.0196
0.9998
0.0000
0.7071
0.7071
-0.0000
0.0000
0.0000
1.0000
0.5443
0.0000
0.8389
0.0000
0.5544
0.8323
Axis
-0.7071
0.7071
-0.0000
1.0000
0.0000
-0.0000
-0.8389
0.0000
0.5443
-1.0000
0.0000
0.0000
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane